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This paper presents a free-field method for inverse estimation of acoustic porous material parameters from sound pressure measurements above small rectangular samples. The finite sample effect, the spherical propagation of the sound field, and a potential lateral material reaction are considered. Using an extensive series of systematically varied finite element simulations, neural network models are developed to replace computationally expensive simulations as a forward model for the calculation of the complex sound pressure above small samples in the inverse optimization. The method is experimentally validated using various porous material samples. The results show that the influence of the finite sample size is successfully removed and thus, the acoustic properties of the materials can be estimated from the determined porous parameters with high accuracy, even based on a single sound pressure measurement over small samples with pronounced edge diffraction. The poroacoustic parameters hence derived can be used directly, e.g., in simulation applications, or to calculate complex surface impedances or absorption coefficients. [ABSTRACT FROM AUTHOR]